List questions from localization

Published on 25 Mar 2026 - 22:11

252

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Let A be a UFD and $A_{P}$ be the localisation of $A$ at prime ideal $P$. Then prove that $A_{P}$ is principal

Published on 11 Nov 2020 - 8:45

122

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Example of graded module which is not flat

Published on 26 Mar 2026 - 12:51

825

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Show that the ring of formal power series is a Euclidean domain.

Published on 27 Mar 2026 - 4:18

60

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Every $R$-linear map of $S^{-1} R$ Modules is automatically a $R_S$-linear map

Published on 18 Nov 2020 - 19:37

375

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Is the ring of the polynomials on a finite algebraic set always a product of local rings?

Published on 18 Nov 2020 - 20:35

217

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Show that $R^* = R\setminus \mathfrak{m}.$

Published on 29 Mar 2026 - 0:06

56

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localization in 2-categories with 2-morphisms

Published on 30 Mar 2026 - 8:29

976

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Show that if $\mathfrak{p} \subset R$ is a prime ideal, then $S = R \setminus \mathfrak{p}$ is multiplicatively closed.

Published on 29 Mar 2026 - 4:44

43

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Proving that $R_{(0)}$ is the field of fractions.

Published on 20 Nov 2020 - 8:38

150

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Localisation of a polynomial ring

Published on 22 Nov 2020 - 11:45

47

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The contraction of $B_p\cdot q$ is $p\cdot A_p$

Published on 24 Nov 2020 - 1:23

75

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Localization by a prime ideal

Published on 28 Nov 2020 - 17:30

77

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Possible Characterization of localization of $\mathbb{Q}[x, y]$

Published on 30 Nov 2020 - 22:04

218

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Localisation of an integral domain

Published on 29 Mar 2026 - 4:48

List Question

Find location of a point on an oval shape

Let A be a UFD and $A_{P}$ be the localisation of $A$ at prime ideal $P$. Then prove that $A_{P}$ is principal

Example of graded module which is not flat

Show that the ring of formal power series is a Euclidean domain.

Every $R$-linear map of $S^{-1} R$ Modules is automatically a $R_S$-linear map

Is the ring of the polynomials on a finite algebraic set always a product of local rings?

Show that $R^* = R\setminus \mathfrak{m}.$

localization in 2-categories with 2-morphisms

Show that if $\mathfrak{p} \subset R$ is a prime ideal, then $S = R \setminus \mathfrak{p}$ is multiplicatively closed.

Proving that $R_{(0)}$ is the field of fractions.

Localisation of a polynomial ring

The contraction of $B_p\cdot q$ is $p\cdot A_p$

Localization by a prime ideal

Possible Characterization of localization of $\mathbb{Q}[x, y]$

Localisation of an integral domain

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